The reason I bet only $1 on the flop instead of about $1.50 was specifically so that I could get away from my hand in case a club hit the turn, rather than making myself pot-committed.
I don't think that there are any more than maybe 9 combos of 1 club hands in the villains' range that we have to worry about, given the line he took (probably 77-99 is about it). And each 1 club combo only has a ~20% chance of improving on the river. Therefore, I don't think that we have to worry about checking the turn to "let the villain catch up". Most of the time, the villain has either 2 clubs or 0 clubs (either a suited combo with clubs or a suited combo without clubs or a pocket pair that already hit a boat/quads).
Going by the pot odds
we're getting, we need to win at least 33% of the time to justify shoving the turn (assuming the villain never folds).
Are we really ahead here enough of the time to justify shoving the turn? I can count 25 combos that the villain could realistically have that beat us: 1 combo of quads (44), 6 combos of boats (3 x 22 and 3 x TT) and 16 combos of flushes (A3, A5, A6, A7, A8, A9, AJ, AQ, AK, KQ, KJ, QJ, J9, 98, 87, 76). I can see the UTG villain flat-calling with all of these hands under the expectation that the CO villain will also flat-call behind and he'll get decent implied odds.
What about hands which beat us: there are 6 combos of JJ, 3 combos of ATs, 3 combos of KTs, 1 combo of QTs, 3 combos of JTs, 3 combos of T9s, 6 combos of 99, 6 combos of 88 and 6 combos of 77. I would expect anything below about 77 is going to fold the flop, since the UTG villain has to worry about the CO villain acting behind. So that makes 37 combos in total.
Now, there might appear to be 37 combos of hands that we beat that would get to the turn this way, but what percentage of the time do you expect these hands to be betting? Moreso, what percentage of the time is the villain going to bet so small instead of shoving? It doesn't look like he's not making this bet for fold equity. It looks exactly like he wants to have a "bet some now, bet the rest on the river" mentality, as if he wants to encourage me to call and doesn't want to scare me off a hand. There's a chance he does this with any random Tx hand, but I'm going to guess that that chance is somewhere around the 25% mark (the other 75% of the time he either checks back or shoves). So that means he's only doing this with 9 combos on average. This just looks like a boat/quads/flush that doesn't want to scare me into folding far more often than a Tx hand or low pocket pair betting for protection.
Let's also suppose that we have very little equity when we're behind and almost 100% equity when we're ahead (the equity probably evens itself out anyway, so we can just simplify things to winning vs losing on the turn). That means that we can expect to win 9/34 times but expect to lose 25/34 times. We're not ahead 33% of the time and thus we should fold to his turn bet.
Is there anything wrong with the logic I used? I obviously didn't do all this maths in my head at the time of making the decision, but I did guess that there were a lot of flush combos in his range and his flop calling range can't be too wide, given the CO villain acting behind. And the sizing of the turn bet just looked so suspicious to me, like he really wanted me to call. I'm not usually this nitty, but it just looked like I was beaten so often on this board texture, given the action.